Frequency-dependent processing and interpretation (FDPI) of seismic data for identifying, imaging and monitoring fluid-saturated underground reservoirs

ABSTRACT

A method for identifying, imaging and monitoring dry or fluid-saturated underground reservoirs using seismic waves reflected from target porous or fractured layers is set forth. Seismic imaging the porous or fractured layer occurs by low pass filtering of the windowed reflections from the target porous or fractured layers leaving frequencies below low-most corner (or full width at half maximum) of a recorded frequency spectra. Additionally, the ratio of image amplitudes is shown to be approximately proportional to reservoir permeability, viscosity of fluid, and the fluid saturation of the porous or fractured layers.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSOREDRESEARCH AND DEVELOPMENT

This invention was made with U.S. Government support under ContractNumber DE-AC03-76SF00098 between the U.S. Department of Energy and TheRegents of the University of California for the management and operationof the Lawrence Berkeley National Laboratory. The U.S. Government hascertain rights in this invention.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority from U.S. patent application Ser. No.10/137,201, filed Apr. 30, 2002 entitled Frequency Dependent Processingand Interpretation (FDPI) of Seismic Data for Identification, Imaging,and Monitoring of Fluid Saturated Underground Reservoirs, which in turnclaims priority from U.S. Provisional Patent Application Ser. No.60/287,446, filed Apr. 30, 2001 entitled Frequency Dependent Processingand Interpretation (FDPI) of Seismic Data for Identification, Imaging,and Monitoring of Fluid Saturated Underground Reservoirs, both of whichare hereby incorporated by reference in their entireties.

BACKGROUND OF THE INVENTION

Identification, imaging and monitoring of fluid-saturated undergroundreservoirs is a very important application of seismic methods. It helpsfind and contour gas and oil deposits, which are usually attributed tofluid-saturated porous or fractured geological layers. It also hasimportant applications for underground water reservoir imaging,estimation of contamination zones, and monitoring of underground gasstorage, as well as for addressing the global issue of CO₂sequestration. The current very high percentage of “dry” drilledindustry wells may be substantially lowered if a more accurate imagingmethod can be found.

It is commonly known and accepted that thin layers in the earth (withthicknesses less than a fraction of a dominant wavelength [λ]) ofseismic waves are invisible to imaging using seismic waves. Wavesreflected from a bottom and a top of such a layer have opposite signsand nearly equal amplitudes. The result is that such waves almost cancelone another, resulting in the layer being obscured in the seismic data.Typically this means that traditional seismic methods cannot imagelayers less than 10 meters thick.

The relationship between seismic response and fluid saturation in areservoir depends on many factors, such as porosity and permeability ofthe reservoir rocks, viscosity and compressibility of the fluid,reservoir thickness and physical properties of the surrounding medium.(See “Seismic Wave Attenuation,” 1981, Geophysics reprint series, No. 2:SEG, D. H. Jonson and M. N. Toksoz, editors.). But there is some generalconnection between the character of porous layer saturation and seismicresponse. In particular, comparing cases of water and gas saturation,phase shifts and energy redistribution between different frequencies areknown. (See Goloshubin, G. M. et al., 1996, “Laboratory experiments ofseismic monitoring,” 58th EAEG Meeting, Amsterdam, and Goloshubin, G.M., and Bakulin, A. V., 1998, “Seismic reflectivity of a thin porousfluid-saturated layer versus frequency” 68th SEG Meeting, New Orleans,976–979.]

Experimental studies have shown that intrinsic attenuation is stronglyaffected by the porous media and fluid saturation. (See Hauge, P. S.,1981, “Measurements of attenuation from vertical seismic profiles”Geophysics, 46, 1548–1558; Raikes, S. A. and White, J. E., 1984,“Measurements of earth attenuation from downhole and surface seismicrecording” Geophysical Prospecting, 32, 892–919; “Seismic WaveAttenuation,” 1981, Geophysics reprint series, No. 2: SEG, D. H. Jonsonand M. N. Toksoz, editors; Sams, M. S. et al., 1997, “The measurement ofvelocity dispersion and frequency-dependent intrinsic attenuation insedimentary rocks,” Geophysics, 62, 1456–1464; Dasgupta, R. and Clarc,R. A, 1998, “Estimation of Q from surface seismic reflection data,”Geophysics, 63, 2120–2128; Goloshubin, G. M. and Korneev, V. A., 2000,“Seismic low frequency effects for fluid-saturated porous media,”Expanded Abstracts, SEG Meeting, Calgary, 976–979.)

It is well accepted that the nondimensional attenuation quality factor Qis frequency-dependent and changes dramatically with liquid saturationand may be less than 10 in sedimentary rocks (See Jones, T. D., 1986,“Pore fluids and frequency-dependent wave propagation in rocks,”Geophysics, 51, 1939–1953, and Sams [above]). Fluid may lower Q inmetamorphic rocks (Pujol, J. M. et al., 1998, “Seismic wave attenuationin metamorphic rocks from VSP data recorded in Germany's continentalsuper-deep borehole,” Geophysics, 63, 354–365) down to 14 and inlimestone (Gadoret, T. et al., 1998, “Fluid distribution effects onsonic attenuation in partially saturated limestones,” Geophysics, 63,154–160) from 200 (dry) to 20–40 (water-saturated).

It is also typically accepted in seismology that attenuation qualityfactor Q usually has values well above 20, which means that it takesmore than 20 wavelengths for a wave to propagate before its amplitude isreduced by more than a half of an original value.

DISCOVERY

We have discovered the existence of very low, high attenuation, qualityfactor Q (Q<5) as a local value for a fluid-saturated porous orfractured layer interrogated by low frequency seismic waves. Typicalseismic measurements give much higher values of Q over such a regionbecause they represent average effective values where the thin layershave a very small contribution. Investigation of such layers at the lowfrequency portion of the exciting seismic waves reveals, for a thinlayer with high attenuation (low Q), that waves are reflected from thetop and the bottom of the layer with very dissimilar amplitudes. Thesedissimilar amplitudes do not cancel each other, and thereby render thethin layer detectable. Specifically, for saturated porous layers, asfrequency decreases, attenuation increases.

Two other important observed features of reflected seismic waves fromfluid-saturated porous layers have been discovered. First, thelow-frequency portions of the exciting seismic vibrations includestronger reflections at the low frequencies. Second, an apparentanomalous velocity dispersion occurs in the reflected waves where highfrequencies arrive earlier than low frequencies. These properties havebeen observed in both laboratory and field seismic data.

The following disclosure stems from a frequency-dependent reflectivityof the fluid-saturated layer by a frictional model with low,frequency-dependent Q values at low frequencies.

BRIEF SUMMARY OF THE INVENTION

A method of identification, imaging and monitoring of fluid-saturatedunderground reservoirs using seismic waves reflected from target porousor fractured layers is set forth. Reflective wave seismic data isprocessed at low frequency spectral portions of the seismic wavesreflected from target porous layers. Frequency-dependent processing andinterpretation (FDPI) is based on use of one or several frequencydependent reflection properties in the vicinity of a low frequencycorner of recorded wave spectra. These properties include: amplitudespectra A (ω), amplitude derivative with respect to frequency

$\frac{\mathbb{d}A}{\mathbb{d}\omega},$phase derivative with respect to frequency D_(P)(ω). It has been foundthat changes in of all these properties in saturated samples, whencompared to unsaturated samples are approximately proportional to boththe fluid viscosity and the fluid saturation of the reservoir. Fluidsaturation and content profiling of an underground layer or reservoir ismade possible by using a two-dimensional (2D) plot.

The frequency dependence of seismic reflections from a thin,fluid-saturated, porous layer has been studied. Reflections from a thin,water-saturated layer was found to have increased amplitude and delayedtravel time at low frequencies for both ultrasonic lab data and seismicfield data. A comparison of these results to laboratory modeling with africtional-viscous theoretical model was then made. The measured datawas best explained by low (Q<5) values of the attenuation parameter Qand its decrease as frequency approaches zero.

At a larger scale, conventional processing of time-lapse VerticalSeismic Profiling (VSP) data found minimal changes in seismic responseof a gas storage reservoir when the reservoir composition changed fromgas- to water-saturated. However, in contrast, by using low-frequencyanalysis, we have found significant seismic reflection attributevariation as a function of frequency. In this case, the reflectionattribute variation was found in the range of 15–50 Hz.

For the low frequencies used here, a proposed explanation suggests thatvery low Q values are present for fluid-saturated porous or fracturedlayers, primarily as a result of internal friction between grains,pores, or fracture walls. The frequency-dependent amplitude and phasereflection properties can be used to detect and monitor liquid saturatedlayers, primarily as a result of internal friction between grains orfracture walls, as well as to detect and monitor liquid-saturated areasin thin porous layers.

This method uses seismic data u(x,t) recorded in space (x) and time (t)for a conventional surface-to-surface, or surface-to-boreholeregistration after standard seismic data pre-processing. Waves w(x,t)reflected from target porous layers should be identified on u(x,t) usingindependent measurements such as borehole core analysis and VerticalSeismic Profiling. Depth localization of the reservoir can also bedetermined by conventional methods using the high frequency parts ofreflected waves. Waves w(x0,t) recorded at location x0 of the boreholerepresent a reference wave. Where no borehole data exists, any targetreflected wave could alternatively be used as a reference wave.

Using the Fourier spectrum W(x,ω) and W(x0,ω) of the functions u(x,t)and u(x0,t), the complex ratio R(x,ω)=W(x,ω)/W(x0,ω) is analyzed forfirst N reliably recorded low frequencies, to compute average relativereflected amplitude

${{A(x)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{R\left( {x,\omega_{i}} \right)}}}}},$the negative of the derivative of the average amplitude with respect tofrequency

${{D_{A}(x)} = {{- \frac{1}{N}}{\sum\limits_{i = 1}^{N}{d{{{R\left( {x,\omega_{i}} \right)}}/d}\;\omega}}}},$and derivative of the average time delay with respect to frequency

${D_{p}(x)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{{d\left( {\arg\left( {{R\left( {x,\omega_{i}} \right)}/\omega_{i}} \right)} \right)}/d}\;{\omega.}}}}$Number N includes all reliably recorded frequencies below the lowfrequency corner of a recorded spectra.

By reliably recorded frequencies, we refer to frequencies whose Fourieramplitudes exceed the noise floor level found in the particular dataset. Such noise floor level is comprised of many sources: source noise,receiver noise, electrical line noise, digitization errors, and in thisinstance reservoir geology. In particular, the reservoir geology cancontribute considerable noise by quarter wavelength

$\frac{\lambda}{4}$frequency addition and cancellation, or tuning effects.

Fluid saturation can be mapped by using any of A(x), D_(A)(x), orD_(P)(x), with calibration conditions A(x₀)=1, D_(A)(x₀)=0, andD_(P)(x₀)=0 at the location x=x₀. A relative change in these fields isapproximately proportional to the viscosity of fluid and the fluidsaturation of the porous or fractured layers. If the saturationcharacteristics data are available for the location x=x₀, in the pointsof drilled wells, then zones with A(x)≈1, D_(A)(x)≈0, and D_(P)(x)≈0 canbe attributed to the same value of saturation.

For monitoring purposes the changes of anomalous zones configurationsindicate the movement of fluid-saturated zones in development andpropagation.

Method Overview

The internal friction dissipation mechanism explains all of the aboveproperties of waves reflected from the porous layers and provides aneffective procedure for imaging such layers. For a one-dimensionalcompressional wave propagation, the equation of motion has the form

$\begin{matrix}{{{\frac{\mathbb{d}^{2}u}{\mathbb{d}t^{2}} - {\beta\frac{\mathbb{d}u}{\mathbb{d}t}} - {\gamma\frac{\mathbb{d}^{2}}{\mathbb{d}x^{2}}\frac{\mathbb{d}u}{\mathbb{d}t}} - {v^{2}\frac{\mathbb{d}^{2}u}{\mathbb{d}x^{2}}}} = 0},} & (1)\end{matrix}$where u is a displacement vector. The first term represents the inertia.The second term in the equation is the frictional dissipative force. Thethird term describes viscous damping. The final term represents elasticportion of the wave propagation. The constants β, and γ are respectivelythe “frictional” and “viscous” attenuation parameters.

In frequency domain, the terms of Equation (1) respectively relate tofrequency (ω) as follows:ω² ω ω³ ω^(2.)As frequency decreases, the frictional dissipative force dominates (ω).Physical interpretation of these parameters (β, and γ) is a separateissue and is not discussed here. Parameter ν is a phase velocity in anon-dissipative medium. An analytical solution of this equation existsand has the formu=e ^(ikx−αx) e ^(iωt)  (2)with wave number k, attenuation coefficient α and angular frequency ω.The attenuation parameter Q is defined through the expressionQ=ω/2αν.  (3)Parameter Q describes the effective dissipation of a medium.

From the structure of Eq. (1), it follows that the frictional termdominates at low frequencies, while the viscous term dominates at highfrequencies; therefore, the viscosity is the main factor responsible forwave dissipation. Substitution of Eq. (2) in Eq. (1) gives the followingexpressions

$\begin{matrix}{{\alpha = \frac{vp}{q}},\mspace{14mu}{k = \frac{\omega\; q}{v}}} & (7) \\{{{{where}\mspace{14mu} q} = \sqrt{\frac{1}{2} - {p\;\gamma} + \sqrt{\frac{1}{4} + {\frac{p}{2}\left( {\frac{v^{2}\beta}{\omega^{2}} - \gamma} \right)}}}},{p = {\frac{1}{2}\frac{{\omega^{2}\gamma} + {v^{2}\beta}}{v^{4} + {\omega^{2}\gamma^{2}}}}}} & (8) \\{{{{When}\mspace{14mu}\gamma} = 0},{q = {\frac{1}{\sqrt{2}}\sqrt{1 + \sqrt{1 + \frac{\beta^{2}}{\omega^{2}}}}}},{p = {{{\frac{\beta}{2v^{2}}.{When}}\mspace{14mu}\beta} < \omega}},{Q \approx \sqrt{{\omega/2}\beta}},{{{while}\mspace{14mu}{for}\mspace{20mu}\omega} > {\beta\mspace{14mu}{we}\mspace{14mu}{have}\mspace{14mu} Q} \approx {\omega/{\beta.}}}} & (9) \\{{{{When}\mspace{14mu}\beta} = 0},\;{q = \sqrt{\frac{1}{2} - {p\;\gamma} + \sqrt{\frac{1}{4} + {\frac{p}{2}\gamma}}}},{p = {\frac{1}{2}\frac{\omega^{2}\gamma}{v^{4} + {\omega^{2}\gamma^{2}}}}},} & (10)\end{matrix}$and Q≈ω⁻¹ at low frequencies.

Thus the decrease of Q at low frequencies can be explained by thepresence of a frictional dissipation mechanism.

The suggested method uses two kinds of frequency-dependent informationabout a wave reflected from target layers: apparent dispersion ofvelocity and dependence of amplitude on frequency. Each of the mappingfunctions A(x), D_(A)(x), and D_(P)(x) can be used independently,although combining two or all three of them brings the most reliableresults. All measurements here are to be done for the lower part ofseismic signal frequencies, when the layer thickness is substantiallyless than a dominant wavelength.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is an elevation view of a laboratory experiment having a source(S) generating a seismic wave for reflection (R) from a porous layerwhere the porous layer has only the right-hand portion of the layersaturated with water;

FIGS. 1B, 1C and 1D are respective seismic profiles using common offsetgathers by difference filtering for dry (FIG. 1C) and water-saturatedcases (FIG. 1D);

FIGS. 2A and 2B are respective laboratory models of a dry porous layerslowly flooded with water from right to left;

FIGS. 2C and 2D are respective vertical seismic profiles of the dryporous layer and the saturated porous layer corresponding to FIGS. 2Aand 2B;

FIG. 3 is a plot of theoretical and experimental attenuation, Q, versusfrequency data, with the experimental data shown in solid lines andtheoretical data being shown in broken lines, demonstrating thatattenuation is greater for water-saturated layers;

FIG. 4 is a plot of reflection coefficient ratios versus frequencycomputed from data for a layer, theory for a layer, and theory for ahalf-space;

FIG. 5 is a plot of travel-time delay versus frequency for awater-saturated layer with respect to a reflection from a dry layer, theupper curve representing theoretical data and the lower curverepresenting experimental data;

FIG. 6 is an experimental setup for a porous layer having respective dryportions, water-saturated portions, and oil-saturated portions;

FIGS. 7A, 7B, and 7C are respective high frequency, low-frequency, andvery low-frequency vertical seismic profiles of the experimental setupof FIG. 6;

FIG. 8 is a two-dimensional stacked seismic section of real data from aWestern Siberian oilfield, using standard processed reflection data fromseismic exploration, with boreholes where oil has been both found andnot found as indicated on the plot;

FIG. 9 is a plot of the same data used in FIG. 8, however now usinglow-frequency processed reflection data according to this invention;

FIG. 10 is a low-frequency reflective image mapping of a water-oilcontact boundary and well content, and shows the region and extent of anoil saturated porous region;

FIG. 11 shows a reflection data amplitude spectrum with thelow-frequency data component being confined to the low frequency portionof the spectrum less than about 3 dB of the maximum value;

FIG. 12 shows a hypothetical reflection data amplitude Fourier spectrumwith the low-frequency data component being confined between a lowerfrequency bounded by a noise floor, and a low frequency corner;

FIG. 13A is a block diagram of traditional seismic analysis using inputdata signal preprocessing, followed by standard processing techniques toyield an output image;

FIG. 13B a block diagram of traditional seismic analysis of FIG. 13Amodified using basis function transformation and just the velocityanalysis of standard processing, followed by a summation of thetransformed output low frequency data component images to yield afrequency dependent output image; and

FIG. 13C shows the traditional seismic analysis method depicted in FIG.13A augmented by frequency dependent processing and interpretationtaught in this invention.

DETAILED DESCRIPTION OF THE INVENTION

Defined Terms

Computer: any device capable of performing the steps developed in thisinvention to result in an optimal waterflood injection, including butnot limited to: a microprocessor, a digital state machine, a fieldprogrammable gate array (FGPA), a digital signal processor, a collocatedintegrated memory system with microprocessor and analog or digitaloutput device, a distributed memory system with microprocessor andanalog or digital output device connected with digital or analog signalprotocols.

Computer readable media: any source of organized information that may beprocessed by a computer to perform the steps developed in this inventionto result in an optimal waterflood injection, including but not limitedto: a magnetically readable storage system; optically readable storagemedia such as punch cards or printed matter readable by direct methodsor methods of optical character recognition; other optical storage mediasuch as a compact disc (CD), a digital versatile disc (DVD), arewritable CD and/or DVD; electrically readable media such asprogrammable read only memories (PROMs), electrically erasableprogrammable read only memories (EEPROMs), field programmable gatearrays (FGPAs), flash random access memory (flash RAM); and remotelytransmitted information transmitted by electromagnetic or opticalmethods.

Standard processing means processing an input data set having the samesample time period. Initially, the data set is preprocessed according totraditional methods. Then the data undergoes velocity analysis toinvestigate a particular layer of the geology. After velocity analysis,a subsequent analysis is done to compute an output image usable for oilexploration or petroleum reservoir analysis. These subsequent analyticaltechniques include traditional stacking, migration, and amplitude versusoffset (AVO) processing.

Preprocessing means applying traditional signal “clean up” operationsused in geological analysis to correct for amplitude variations, timingoffsets, voltage offset, etc. so that the preprocessed data set is readywithout further modification to be input into standard processing.

Basis function transform means a mathematical transformation or mappingof an input signal into a linear combination of mathematical functionsorthogonal over an interval. Such basis functions can be sine and cosinewaves as in Fourier spectral analysis, or other polynomial functionssuch as Bessel, Legendre, trigonometric, or hyperbolic functions. Astandard reference for such orthogonal functions includes Gradshteyn andRyzhik's, “Table of Integral Series and Producst,” Academic Press Inc.,1965. A more recent approach has been used in seismic analysis withwavelet transformation, which used to filter an input signal into alinear combination of wave packets having different center frequenciesand temporal shapes.

Frequency Dependency

The frequency dependence of seismic reflections from a thin,fluid-saturated, porous or fractured layer was considered. Reflectionsfrom a thin, water-saturated layer have increased amplitude and delayedtravel time at low frequencies for both ultrasonic lab data and seismicfield data. The results of laboratory modeling were compared with africtional-viscous theoretical model to find that low (Q<5) values ofthe attenuation parameter Q and its monotonic increase with frequencyexplained the observations.

On a larger scale, conventional processing of time-lapse VSP data foundminimal changes in seismic response of a gas-storage reservoir when thereservoir changed from gas to water-saturated. However, low-frequencyanalysis found significant seismic reflection attribute variation as afunction of frequency, in the range of about 15–50 Hz. Theseobservations corresponded to previously measured effects in laboratorydata and theory. The frequency range below 15 Hz was discarded due tothe noise floor level of this particular instrumentation system andreservoir.

A proposed explanation suggests very low Q values for porous orfractured fluid-saturated layers, primarily as a result of internalfriction between grains or fracture walls. The frequency-dependentamplitude and phase reflection properties presented here can be used fordetecting and monitoring layers, to detect and monitor liquid-saturatedareas in thin porous and fractured layers.

A series of ultrasonic laboratory experiments were used to investigatethe wave fields reflected from and transmitted through a porous layerwith varying water saturation from a source S to a receiver R. Thephysical model (FIG. 1A) consisted of two 3 mm thick Plexiglas sheets Pwith a sealed void filled with porous artificial sandstone. Theartificial sandstone A was prepared using a natural sand and claymixture. The thickness of the artificial sandstone plate was 3 mm and itwas much less than a wavelength. Therefore 2D physical modeling wasused, where the Plexiglas was simulating a homogeneous constant-velocitybackground medium.

The porous layer L in each case was made of artificial sandstone withthe same sizes of sand and clay grains, and was hermetically sealed toallow its saturation by fluid. The experiment found the acousticimpedance of the water-saturated sandstone was higher than the impedanceof non-saturated sandstone. The Plexiglas had the lowest impedance. Theexpected reflection coefficient of the water-saturated sandstone washigher than for the dry sandstone.

The physical modeling data were recorded using experimental setup shownon FIG. 1 for both dry and water saturated sandstone. The layer had a 7mm vertical dimension and had 0.32 porosity and about 300 mDarcypermeability. The velocities and densities of the used materials were:Vp=1700 m/sec, Vs=1025 m/sec, D=1800 kg/m3 (dry layer); Vp=2100 m/sec,Vs=1250 m/sec, D=2500 kg/m3 (water-saturated layer); and Vp=2300 m/sec,Vs=1340 m/sec, D=1200 kg/m3 (Plexiglas).

Waves reflected from the layer were recorded. A significant differenceis seen between the seismic response of the porous, water-saturated zoneand non-saturated (dry) zone (FIG. 1B). The water-saturated zone isdistinguished due to a phase shift and loss of high-frequency energy.The low-frequency “bright spot” is associated with water saturation(FIG. 1D).

VSP observation geometry shown in FIGS. 2B to 2D illustrate one examplefrom the series of experiments. Referring to FIGS. 2A and 2B, thereflection coefficient of the thin (7 mm) layer was investigated using asimilar model to the one set forth in FIG. 1A. This time source Stransmitted to receivers R₁ and R₂. VSP observation geometry is setforth in FIGS. 2C and 2D for the respective dry and water-saturatedlayers. The offset was much smaller than the depth to the layer and thereflection angle was practically equal to zero. There is a substantialdifference between the upgoing wave field from the water-saturated layerand the upgoing wave field from the dry layer, whereas the transmittedfield shows no such difference.

The physical modeling data were recorded using VSP experimental setupshown on FIG. 1 to measure of Q factor vs. frequency in thick porouslayer for both dry and water saturation. The layer was 40 mm thick andhad 0.32 porosity. To measure Q as a function of frequency, a set ofspecial experiments was conducted for a thick porous layer wherereflected and refracted waves could be detected without interference.This was done for both dry and water-saturation cases using the same VSPobservation system shown in FIGS. 2A and 2B. The porous layer ofartificial sandstone was prepared with the same composition of sand andclay as for the previous experiment. In both cases, a transmitted wavewas used to determine Q. The measured values of Q, together with theirtheoretical approximations are shown in FIG. 3. Note thefrequency-dependent, low values of Q.

In FIG. 3, plots of Q versus frequency are shown for dry layers (upperplots) and for water-saturated layers (lower plots). Each set of plotshas experimental data (solid lines) and theoretical data (dashed lines).The values of Q are substantially lower as frequency increases.

Referring to FIG. 4 reflection coefficient ratios versus frequency.Actual data plot 14 matches with theoretical data plot 16. This iscompared with a half space data plot 18 for a half space.

In FIG. 5, a plot of travel-time delay, in microseconds, from awater-saturated layer with respect to a reflection from a dry layer isshown against frequency. Actual data is plotted in curve 20. Thetheoretical data is plotted in curve 22.

Referring to FIG. 6, an experimental model similar to FIG. 1A and FIGS.2A and 2B is shown. Construction of layer L and the model used are thesame as in FIG. 1. Fluid content consists of water W followed by oil O.Physical modeling reflection data was recorded using thesurface-constant offset experimental set up shown FIG. 6 to test thethin porous layer for dry, water-saturated, and oil-saturated cases. Thelayer was 7 mm thick, having 0.32 porosity and about 300 mDarcypermeability. The velocities and densities of the materials were Vp=1700m per second, Vs=1025 m per second, D=1800 kg/m3 (dry porous layer); andVp=2300, Vs=1340, D=1200 (Plexiglas).

In FIG. 7A, a high-frequency plot is illustrated using common offsetgathers by different filtering for dry, water-saturated, and oilsaturated cases. FIG. 7B illustrates a low-frequency plot. In this case,the height of a layer L is between 1 and 0.2 of the interrogated layerin wavelength (λ). Finally, FIG. 7C illustrates the plot for a verylow-frequency, where the height of a layer L is less than 0.2 of theinterrogated layer in wavelength (λ). Note that, with respect to FIG.7B, the water layer is seen. Likewise, in the very low frequencyillustration of FIG. 7C, the oil layer O is prominently displayed.

Following laboratory testing, real data from a West Siberian oil fieldwas taken. FIG. 8 is an illustration of the standard processedreflection data. Water and oil producing wells are both illustrated.

FIG. 9 is an illustration of the identical West Siberian oil field datataken at low frequency in accordance with the teachings of thisdisclosure.

It can be seen that the conventional process data of FIG. 8 has a poorcorrelation with the character of saturation of the oil field. When thatdata is contrasted with the low-frequency processed reflection datashown in FIG. 9, it can be seen that the latter plot gives a goodmapping of oil content.

Referring to FIG. 10, it will be seen that low-frequency processing ofseismic reflection data in three dimensions allows contouring of theoil/water contact within the thin reservoir of another West Siberian oilfield reservoir. Wells #9, 76, 91, 95 were used for seismic fluidattribute calibration. Information for wells #3, 5, 63, 74, 75, 77, 78,79, 86, 96, 101 was disclosed after processing and interpretation fortesting purposes. This testing demonstrated very good oil/water contactcontouring capabilities of the method.

By using the fluid attribute calibration of where oil was found, itappears that a roughly concave region of oil in FIG. 10 is bounded bythe oil/water contact interface. This information can be used forreservoir management so that primary production will initially produceas much of the oil as possible, as well as subsequently in waterfloodsecondary recovery operations.

From the following description, it will be understood that the techniqueof this invention can, in effect, be calibrated by the use ofexploratory boreholes or wells. Specifically, by taking data for anentire reservoir or oil field, the seismic analysis data can be comparedto data determined by boreholes. Using the seismic data from theboreholes, one can equate the probable content and saturation ofsimilarly analyzed seismic data for an oil field to the content andsaturation found at the boreholes.

In the following claims, the reconstruction of reflected seismic wavesto form intelligible images of underground geologic structures isreferred to as “standard processing of recorded reflected seismicwaves.” This term includes commonly used procedures of seismic dataprocessing such as geometric spreading correction, deconvolution,velocity analysis, normal move out and dip move out corrections,stacking, and more complex reconstruction of seismic signals such asmigration, as well as amplitude versus offset analysis. The term “imagefunctions” includes the results of standard processed seismic datarepresented by of one or two horizontal spatial coordinates and timeand/or depth, such as velocity models, time and depth stacked sections,and amplitude variation with offset (AVO) attributes.

Additionally the term is used “frequency dependent data set.” Thisrefers to decomposition of a time-domain low frequency part of arecorded seismic reflection into a set of frequency dependent band passfiltered low frequency time-domain data components. The “low frequencydata component” refers to utilizing the low-frequency portion ofrecorded seismic signals Fourier transformed into spectral amplitude vs.frequency format, and using the data found in the left-hand part of theamplitude versus frequency plot resulting from the recorded seismicwaves frequency spectra below a low frequency corner of that spectra.The low frequency data component begins at the lowest non-noisefrequency, with frequencies below having amplitudes masked by systemnoise discarded. The upper end of the low frequency data component isalso known as the low frequency corner. The low frequency corner istypically bounded at a maximum frequency, which is a lower frequencythan the frequency of the maximum amplitude spectrum, and is found whenthe maximum contrast of the resultant reservoir image is obtained.

For well-behaved Gaussian spectral curves, the low frequency cornerwould typically appear at about 3 db lower than the maximum amplitude ata frequency lower than that of the maximum amplitude. For real reservoirdata with “tuning” effects of geological layered spectral cancellationand reinforcement, the corner could be proportionately less, and bebounded by the peak value of the first local maximum amplitude of thespectral data.

All claimed here methods of seismic interpretation of underground porousor fractured layers comprised of the following preliminary steps aimedfor obtaining frequency dependent data processing results used forsubsequent imaging and called here “obtaining of frequency dependentimage functions”. Referring to FIG. 11, the low frequency datacomponents of reflected seismic data is illustrated. The illustratedgraph plots amplitude against frequency for an ideal seismic reflectedwave. Generally, amplitude spectra of seismic reflections have a varietyof shapes, which depend on several physical parameters, typicallycomprising: a source and a receiver characteristic, a rock medium andwave propagation distance, and a decay approaching to both low or highends of the frequency scale. It will be seen that the illustrated curveincludes a mean M and a low frequency portion L. Low frequency portion Lis here defined is that portion of the total illustrated curve, which isless than minus 3 dB of the total mean value M of the data. When thefollowing claims use the term “low frequency data components”, the lowfrequency portion L is being described. This value is approximately 0.7(or seventy percent 70%) of the mean value M for this idealized Gaussianspectral distribution. This terminology is consistent with that found inthe Encyclopedic Dictionary of Exploration Geophysics, Third Edition byRobert E. Sheriff, © 1991 by the Society of Exploration Geophysicist,especially at the definition of a “filter” as it relates to “band pass.”

Referring to FIG. 12, a lesser well-behaved Gaussian spectral curve isillustrated. The noise floor and an illustrative selection of the lowfrequency data component is given. The noise floor is established byspectral analysis or other methods, as the amplitude that the genericsystem-under-test generates according to normal engineering andpetroleum engineering methods. Once the noise floor is established, thespectral response curve intersected with the noise floor to establish a“LOWER FREQUENCY” and a “HIGHER FREQUENCY.” For the purposes of FDPI, a“MAX USABLE” frequency is established about half way between the lowerand higher frequencies. For most purposes, this is the highest frequencythat will be used as the “LOW FREQUENCY DATA COMPONENT”.

It should be noted that if the entire signal spectrum were to be used,from the lower to higher frequency, then FDPI using frequency dependentstandard processing would yield the same analytical result astraditional seismic standard processing. Since it has previously beenshown that thin layers have decreased response with increasingfrequency, the best benefit of this invention occurs at lowerfrequencies.

Another way to describe this low frequency portion is related to theconcept of the full width half maximum value of the frequencydistribution, or FWHM. However here, the lower frequency value atapproximately seventy percent (70%) of the maximum value (˜3 dBreduction in amplitude) of the curve is used as the low frequencycorner. The low frequency portion of the curve is then that region at orbelow the lower of the low frequency corner. For reference, the FWHM istraditionally the difference between the frequencies on either side of aspectral line curve at which the frequency quantity reaches half of itmaximum value, or is ˜6 dB reduced in amplitude (see McGraw-Hill,Dictionary of Scientific and Technical Terms, Fifth Edition, 1993).

Thus, a method of seismic interpretation of underground porous orfractured layers is disclosed where seismic waves have been directed toan underground target porous or fractured layers and reflected seismicwaves from the underground target porous or fractured layers have beenrecorded according to FIG. 11. First, a plurality of frequency dependentdata sets is computed for the low frequency data components at or belowthe lower of the FWHM frequency value. In the illustration of FIG. 11, apreferred number of six subsets of frequency dependent data sets hasbeen computed. Thereafter, the velocity for each frequency dependentdata set is computed to obtain a frequency dependent velocity. Finally,these frequency dependent velocities are imaged using a frequency andaverage derivative of the velocities with respect to frequency. As hasbeen set forth with respect to FIGS. 9 and 10, the obtained data may becalibrated using well data.

FIGS. 13 A, B, and C show the relationship between frequency dependentprocessing and traditional seismic analysis techniques. FIG. 13A showstraditional seismic analysis where preprocessed data signals are inputinto a standard processing package. After velocity analysis, a secondanalysis is done using stacking, migration, or amplitude versus offset(AVO) to generate an output image. Traditional standard processing usesthe preprocessed input data signals as a single data set.

FIG. 13B augments the traditional seismic analysis techniques of FIG.13A with an initial basis function transformation prior to velocityanalysis. All of the FIGS. 13 A, B, and C represent simplifiedillustrative rough functional blocks. Actual computer code representingthe implementation is more complicated and hence more difficult tocomprehend due to multiply nested looping and optimization to reducecomputation time to the minimum low frequency data component wherepossible. The simplified illustrative rough functional blocks moreclearly indicate the boundaries between prior art and this invention.

Referring to FIG. 13B, the basis function transforms the preprocessedinput data time-based signals into a bandpass frequency dependent dataset. These basis functions can be of virtually any type, so long as theygenerate a filtered output about some given frequency. For example, awavelet transformation may be used for each of the center frequenciesstarting at

$\frac{1}{T}$and continuing up to

$\frac{n}{T}$for the i=1,2, . . . n data. Thus, input preprocessed input datatime-based signals are effectively bandpass filtered about the centerfrequency of the wavelet. This resulting filtered data set is thenpassed through velocity analysis, and results in one component of thetransformed output image. When each of the frequencies of the lowfrequency data component is processed and added together, a resultantoutput image is obtained.

Since each of the bandpass filtered velocity components represent avelocity at a specific center frequency, successive transformed outputimages may be numerically differentiated according to widely knownnumerical analysis techniques to yield an image of the derivative withrespect to frequency.

In FIG. 13C, the fullest implementation of this invention is described.Here, input preprocessed data signals are basis function transformed ata particular center frequency, passed into velocity analysis, then intoany of stacking, migration, or amplitude versus offset (AVO) analysis toproduce a single frequency dependent frame of a transformed outputimage. As the center frequency is incremented through the spectral rangeof the low frequency data component, more transformed output imageframes are accumulated. After all of the low frequency data componentframes have been processed, the individual frames are added to producean output image. As described before, the low frequency corner of thelow frequency data component can be increased up to a max usablefrequency, or reduced to as low as the lower frequency to produce anoutput image with best contrast.

FIG. 13C can be used to produce an optimal contrast output image forstacking, migration, and AVO. Additionally, derivative of velocity withrespect to frequency can also be used to generate an optimal contrastoutput image. It is the inventor's experience that depending on thereservoir geology and the data therein, each of these four analyticalmethods may produce the best of the optimal contrast output images.

Additionally, a method of seismic interpretation of underground porousor fractured layers includes the computing of a plurality of frequencydependent data sets for low frequency data components. Standard imageprocessing of each frequency dependent data set is used to obtainfrequency dependent image functions. Thereafter, frequency dependentimage functions for low frequency data components are obtained. Finally,imaging of the porous or fractured layer utilizing a frequency averagederivative of the image functions over frequency is utilized. Again,obtained well data may be used for calibration.

Further, a method of seismic interpretation of underground porous orfractured layers again includes computing a plurality of frequencydependent data sets for low frequency data components. Thereafter,standard processing of each frequency dependent data set is utilized toobtain frequency dependent image functions. As to the low frequency datacomponents, frequency dependent image functions are obtained for the lowfrequency data components. Imaging of the porous or fractured layerusing the frequency average of the image function occurs.

A method of seismic mapping of underground porous or fractured layers isalso disclosed. In this technique, a target reflection is selected fromthe seismic mapping of underground porous or fractured layers.Thereafter, taking of reference amplitudes and a reference arrival timesof the target reflection occurs using image functions computed forfrequencies above a low frequency corner. Next, frequency dependantimage functions are obtained for the target reflection for the lowfrequency data components. Finally, mapping of the porous or fracturedlayer using a ratio of the frequency average image of the low frequencydata components to reference amplitude occurs. Again, extant well datacan be used to calibrating the resultant image.

Further, and as described in the immediately preceding variant of thistechnique, a target reflection may be selected from an image functionfor the seismic mapping of underground or porous fractured layers.Reference amplitude and reference arrival times of the target reflectionare picked using image functions computed for frequencies above the lowfrequency corner. Thereafter, frequency dependant image functions forthe target reflection are obtained for the low frequency datacomponents. Finally, mapping of the porous or fractured layer using adifference of the frequency average image of the low frequency datacomponents and reference amplitudes is utilized.

As an additional variant, a method of seismic mapping of undergroundporous or fractured layers includes selecting of a target reflection inand image function. Thereafter, arrival times of the target reflectionusing image functions computed for frequencies above the low frequencycorner are utilized. Next, frequency dependent image functions for thetarget reflection for using the low frequency data components are made.Taking the low frequency arrival times of the target reflectionutilizing the frequency dependant image function follows. Finally,mapping of the porous or fractured layer using the difference of thefrequency average of the low frequency arrival times and referencearrival times occurs. Again, and as applicable to all of theabove-described variations, actual well data may be utilized to processand calibrate the image.

The readers attention is directed to FIGS. 9 and 10. These images ofunderground fractured or porous layers have never existed before theadvent of the technique described herein. For the first time, we havebeen able to reliably image narrow underground porous or fracturedlayers. Further, by utilizing extant bore hole information, acorrelating that information with the images obtained, liquid finds at abore hole can be extracted to other parts of an image with highreliability. Thus, the produced images (or maps) of the seismic data arehighly useful manufactured articles utilizing this technique.

It is believed that the image of FIG. 10 is especially instructive inthis regard. The imaged field of the porous or fractured layers willtypically be the subject of state of the art advanced oil extractiontechniques. These techniques will include the drilling for oil and theinjection of fluids (usually containing water) to assist in theextraction of oil.

Extracting oil in the wrong location limits useful well life and can bea detriment to the potential production of a whole field. Further,injecting fluid at the wrong location can shorten the utility of adrilled well and even be detrimental to the total possible production ofthe oil field. The image produced by this technique leverages theability of those skilled in oil or gas extraction to obtain a precisethree-dimensional topographic plot of an interrogated field. Thisenables the best possible judgments to be exercised in both fluidextraction from and fluid injection to a seismically interrogated fieldin accordance with this disclosure. While we do not attempt to disclosehow that judgment should be exercised, we do provide a superior imagearticle from which such judgments can be based.

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication or patent application were eachspecifically and individually indicated to be incorporated by reference.

The description given here, and best modes of operation of theinvention, are not intended to limit the scope of the invention. Manymodifications, alternative constructions, and equivalents may beemployed without departing from the scope and spirit of the invention.

1. A method of seismic interpretation of underground porous or fracturedlayers where seismic waves have been directed to an underground targetporous or fractured layers and reflected seismic waves from theunderground target porous or fractured layers have been recorded, themethod comprising the steps of: computing of a plurality of frequencydependent data sets for a low frequency data component; computingvelocity for each frequency dependent data set to obtain a set offrequency dependent velocities; and, imaging the porous or fracturedlayer using a derivative of velocity with respect to frequency.
 2. Themethod of seismic interpretation of underground porous or fracturedlayers according to claim 1 and including: calibrating of obtainedimages using well data.
 3. A method of seismic interpretation ofunderground porous or fractured layers comprising the steps of:computing of a plurality of frequency dependent data sets for lowfrequency data component; standard processing of each frequencydependent data set to obtain frequency dependent image functions;obtaining frequency dependent image functions for low frequency datacomponents; and, imaging the porous or fractured layer using a frequencyaverage derivative of the image functions with respect to frequency. 4.The method of seismic interpretation of underground porous or fracturedlayers according to claim 3 and wherein: calibration of the images usingwell data.
 5. A method of seismic interpretation of underground porousor fractured layers comprising the steps of: computing of a plurality offrequency dependent data sets for low frequency data component; standardprocessing of each frequency dependent data set to obtain frequencydependent image functions; obtaining frequency dependent image functionsfor low frequency data components; and, imaging the porous or fracturedlayer using the frequency average of the image functions.
 6. The methodof seismic interpretation of underground porous or fractured layersaccording to claim 5 and including: calibrating the obtained imagesusing well data.
 7. A method of seismic mapping of underground porous orfractured layers comprising the steps of: selecting a target reflectionin an image function from the seismic mapping of underground porous orfractured layers; selecting reference amplitudes and reference arrivaltimes of the target reflection using image functions computed forfrequencies above a low frequency corner; obtaining of frequencydependent image functions for the target reflection for the lowfrequency data component; and, mapping of the porous or fractured layerusing ratio of the frequency average image of low frequency datacomponent to reference amplitude.
 8. The method of seismic mapping ofunderground porous or fractured layers according to claim 7 andincluding: calibrating the obtained images using well data.
 9. A methodof seismic mapping of underground porous or fractured layers comprisingthe steps of: selecting a target reflection in an image function fromthe seismic mapping of underground porous or fractured layers; pickingof reference amplitudes and reference arrival times of the targetreflection using image functions computed for frequencies above a lowfrequency corner; obtaining of frequency dependent image functions forthe target reflection for the low frequency data component; and, mappingof the porous or fractured layer using a difference of the frequencyaverage image of low frequency data component and reference amplitudes.10. The method of seismic mapping of underground porous or fracturedlayers according to claim 9 and including: calibrating the obtainedimages using well data.
 11. A method of frequency dependent seismic oildetection, comprising the steps of: acquiring a preprocessed input datasignal set; transforming the preprocessed input data signal set into afrequency filtered data set by using one of a plurality of basistransformation functions; standard processing of the frequency filtereddata set to produce a plurality of transformed output images, each forthe corresponding basis transformation function; determining a lowfrequency data component above a noise floor bounded by a lowerfrequency and a low frequency corner; and summing the transformed outputimages from the lower frequency to the low frequency corner to generatean output image with an output image contrast.
 12. The method offrequency dependent seismic oil detection of claim 11, furthercomprising the steps of: outputting the output image for subsequent oildetection.
 13. The method of frequency dependent seismic oil detectionof claim 12, further comprising the steps of: a. varying the lowfrequency corner from a max usable frequency to the lower frequency todetermine an improved output image contrast for subsequent oildetection.
 14. The method of frequency dependent seismic oil detectionof claim 13, wherein standard processing further comprises the steps of:computing a velocity analysis producing a frequency dependent velocityanalyzed image; and computing the transformed output image by one of themethods of the group: stacking; migration; amplitude versus offset;numerical differentiation of the frequency dependent velocity analyzedimage to produce a derivative with respect to frequency.
 15. The methodof frequency dependent seismic oil detection of claim 14, wherein thetransforming step further comprises: applying one of the group of: aFourier transform, a wavelet transform, and a bandpass functiontransform.
 16. The method of frequency dependent seismic oil detectionof claim 15, wherein the summing step further comprises: applying one ofthe group of operations to calculate: a reflected amplitude ratio, aderivative of time delay with respect to frequency, a derivative ofvelocity with respect to frequency, a derivative of amplitude withrespect to frequency, and a derivative of phase with respect tofrequency.
 17. The method of frequency dependent seismic oil detectionof claim 16 further comprising the step of: storing the output imagehaving the improved output image contrast in a computer-readable medium.18. The method of frequency dependent seismic oil detection of claim 17further comprising the steps of: storing the output image having theoptimal output image contrast in a computer-readable medium.
 19. Themethod of frequency dependent seismic oil detection of claim 18 furthercomprising the step of; storing as a computer program in at least onecomputer-readable medium, said steps from acquiring a preprocessed inputdata signal set through storing the output image.